Question

Сократить дробь 5/(1+³√(32cos⁴15°-10-8√3))

Answer 1

Решение на фото...........................

Answer 2

To simplify the fraction 5/(1 + ³√(32cos⁴15° - 10 - 8√3)), we first need to calculate the value inside the cube root and then add it to 1. Here are the steps to simplify the expression:

Step 1: Calculate the value inside the cube root Given: cos(15°) = √3 + √2 / 4

32cos⁴(15°) - 10 - 8√3 = 32 * ((√3 + √2 / 4)²) - 10 - 8√3 = 32 * ((3 + 2√6 + 2/4) / 16) - 10 - 8√3 = 32 * ((3 + 2√6 + 0.5) / 16) - 10 - 8√3 = (3 + 2√6 + 0.5) / 0.5 - 10 - 8√3 = 6 + 4√6 + 1 - 10 - 8√3 = -3 + 4√6 - 8√3

Step 2: Add 1 to the value inside the cube root 1 + ³√(-3 + 4√6 - 8√3)

Now, the fraction becomes:

5 / (1 + ³√(-3 + 4√6 - 8√3))

Note: At this point, the expression cannot be simplified further since the cube root term contains radicals. The fraction is now in its simplest form.